Welcome,
Guest
. Please
login
or
register
.
Did you miss your
activation email
?
1 Hour
1 Day
1 Week
1 Month
Forever
Login with username, password and session length
Home
About
Team
Rules
Stats
Status
Sitemap
Chat
Downloads
Forum
News
Our Projects
Major Community Projects
Recent Posts
Unread Posts
Replies
Tools
SourceCoder3
Other Things...
Omnimaga Radio
TI83 Plus ASM File Unsquisher
Z80 Conversion Tools
IES TI File Editor
Free RAM areas
Comprehensive Getkeyr table
URL Shortener
Online Axe Tilemap Editor
Help
Contact Us
Change Request
Report Issue/Bug
Team
Articles
Members
View the memberlist
Search For Members
Buddies
Login
Register
Omnimaga
»
Forum
»
General Discussion
»
Other Discussions
»
Math and Science
»
Calculus help?
« previous
next »
Print
Pages: [
1
]
Go Down
Author
Topic: Calculus help? (Read 12878 times)
0 Members and 1 Guest are viewing this topic.
Yeong
Not a bridge
LV12
Extreme Poster (Next: 5000)
Posts: 3739
Rating: +278/12
Survivor of Apocalypse
Calculus help?
«
on:
September 21, 2011, 07:59:46 pm »
Ok. I confronted some question in Calculus class. I guessed the answers right, but I don't know how to get the answer.. XP
Here's the question:
Find 2 lines that are both tangent of graph y=x
^{2}
and y=x
^{2}
+6x5.
Ans: y=2x1, y=4x4
I really got these right by guessing but I need proving. help! XP
Logged
Sig wipe!
chattahippie
LV6
Super Member (Next: 500)
Posts: 358
Rating: +27/0
Super Member! :D
Re: Calculus help?
«
Reply #1 on:
September 21, 2011, 08:05:09 pm »
You find two points that only touch the two equations once each (a tangent), then calculate the slope for each using the slope formula, then b.
y2y1
 = m
x2x1
Both of those lines touch each equation only once, making them each tangent to both y = x^2 and y = x^2 + 6x  5
Hope that helps
Logged
Yeong
Not a bridge
LV12
Extreme Poster (Next: 5000)
Posts: 3739
Rating: +278/12
Survivor of Apocalypse
Re: Calculus help?
«
Reply #2 on:
September 21, 2011, 08:06:55 pm »
But in that way can't you get more than 2 lines?
The answer was only those two line, and no more.
Logged
Sig wipe!
fb39ca4
LV10
31337 u53r (Next: 2000)
Posts: 1749
Rating: +60/3
Re: Calculus help?
«
Reply #3 on:
September 21, 2011, 08:09:56 pm »
No, because there are two pairs of two points each that will create tangent lines. If you mix and match points between the pairs, you will get lines that are not tangent.
Logged
chattahippie
LV6
Super Member (Next: 500)
Posts: 358
Rating: +27/0
Super Member! :D
Re: Calculus help?
«
Reply #4 on:
September 21, 2011, 08:12:17 pm »
You have to make sure that the points you chose only touch each x^2 equation once, and stay on the outside edge, because if they were on the inside they would intersect each equation in 2 places. That narrows down the selection a lot, especially when you are dealing with tangents that must be tangent to two functions/equations. I'm actually not in calculus, but I really like math and from looking intensely at a 96 x 64 graph of all four equations, it does seem that those two lines are the only lines that perfectly work.
Logged
Yeong
Not a bridge
LV12
Extreme Poster (Next: 5000)
Posts: 3739
Rating: +278/12
Survivor of Apocalypse
Re: Calculus help?
«
Reply #5 on:
September 21, 2011, 08:25:12 pm »
That's how I got my answer too. XP
But I need algebraic solution...
(My teacher will ask us)
Logged
Sig wipe!
Xeda112358
they/them
Moderator
LV12
Extreme Poster (Next: 5000)
Posts: 4704
Rating: +719/6
Calculator, do doo doo do do do.
Re: Calculus help?
«
Reply #6 on:
September 21, 2011, 08:29:17 pm »
I will try to work out a way, but I also notice that the second equation is (x1)(x5) if that helps...
Logged
My pastebin

Pokémon Amber

Grammer Programming Language

BatLib Library

Jade Simulator

Zeda's Hex Opcodes

FileSyst Library

CopyProg

TPROG

GroupRead

Lbl Read/Write

Z80 Floating Point Routines
(
z80float on GitHub
)
Z80 Optimized Routines Repository
Yeong
Not a bridge
LV12
Extreme Poster (Next: 5000)
Posts: 3739
Rating: +278/12
Survivor of Apocalypse
Re: Calculus help?
«
Reply #7 on:
September 21, 2011, 08:30:03 pm »
I tried that but that didn't help any.. XP
setting both equations' derivation equal didn't worked either XP
I don't know what to start with XP
Logged
Sig wipe!
chattahippie
LV6
Super Member (Next: 500)
Posts: 358
Rating: +27/0
Super Member! :D
Re: Calculus help?
«
Reply #8 on:
September 21, 2011, 08:55:26 pm »
Well, I guess this can be tied to circles. Circles can only have 2 tangent lines if they aren't touching.
Maybe the same rule applies for parabolas whose curves are in opposite directions?
Logged
sqrt(Time)
LV2
Member (Next: 40)
Posts: 37
Rating: +4/0
Re: Calculus help?
«
Reply #9 on:
September 21, 2011, 08:56:19 pm »
I'm not sure this is the most elegant way of solving it, but it sure should work...
Call the place where it touches the first curve (a,a^2). You find the derivative at the point a, and so you can find the slope and yintercept of the line 
as a function of a
. You should have something like
m=f(a)
intercept=g(a)
Now call the place where it touches the second curve (b,b^2 + 6b 5). You can also find the derivative there, and find the slope and intercept as a function of b, too  something like m=h(b) and intercept=i(b).
So now you have
f(a)=h(b)
g(a)=i(b)
Solve these two equations for a and b, then plug either of one of those into your functions to get the slope and intercept of the lines.
Spoiler
For
Spoiler
:
f(a) and h(b) should be linear, and g(a) and i(b) should be quadratic.
Logged
phenomist
LV4
Regular (Next: 200)
Posts: 132
Rating: +46/3
Re: Calculus help?
«
Reply #10 on:
September 23, 2011, 01:20:47 am »
Another method might be to note that both parabolas have the same curvature, only negated. Their vertex points are at (0,0) and (3,4). Hence, any line tangent to both parabolas must lie on the midpoint of their vertices (1.5,2), which can be easily shown by rotating the diagram.
Considering the tangent line at (a,a^2) has a slope of 2a, we can equate slopes:
(a^22)/(a1.5)=2a => a^22 = 2a^23a => a^23a+2=0 => a=1 or 2.
These generate the desired lines, of slopes 2 and 4.
Logged
Level Designer for Graviter
[Disclaimer: I can't program for my life.]
Print
Pages: [
1
]
Go Up
« previous
next »
Omnimaga
»
Forum
»
General Discussion
»
Other Discussions
»
Math and Science
»
Calculus help?